Functional Analysis (4L, 2E) Prof. Wachsmuth, Nicolas Borchard
Attention
Please register for this module via Moodle before the start of the semester.
Contents
This course teaches the basics of (linear) functional analysis. In particular, we will cover the following topics:
- Metric spaces
- Banach and Hilbert spaces, Lp-spaces, Sobolev spaces
- Linear continuous operators
- Linear functionals, dual spaces, the Hahn-Banach theorem
- Principle of uniform boundedness, closed graph theorem, inverse mapping theorem, open mapping theorem
- Fredholm theory
- Spectral theory
Associated module: 13844; Further information and working materials for the module will be provided via Moodle.
Prior knowledge
Basic knowledge of analysis, linear algebra and measure theory (as covered in a stochastics course).
Examination
In order to take a module examination, an oral examination takes place after the lecture period.
Supplementary literature
The following books are a good supplement to the lecture, in particular they also contain many exercises and further material. Within the BTU Cottbus-Senftenberg they are available free of charge as e-books (see links) and some are available in the library.
- Winfried Kaballo, Grundkurs Funktionalanalysis, Springer, 2018
- Hans Wilhelm Alt, Lineare Funktionalanalysis, Springer, 2016
- Dirk Werner, Funktionalanalysis, Springer, 2011
- Manfred Dobrowolski, Angewandte Funktionalanalysis, Springer, 2010
- Martin Brokate and Götz Kersting, Maß und Integral, Springer, 2011
- Haim Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011
- John B. Conway, A Course in Functional Analysis, Springer, 2007
- Kôsaku Yosida, Functional Analysis, Springer, 1995
- Terry Tao, An Introduction to Measure Theory, AMS, 2011